ON THE EXISTENCE OF LINEAR OPTIMAL-CONTROL WITH OUTPUT-FEEDBACK

A necessary and sufficient condition is established for the existence of an output feedback u = -Ky that is LQ optimal with respect to some nonsingular quadratic cost, a fact that entails robustness in the closed-loop systems. It is shown that if the system (with equal number of inputs and outputs) is strict minimum phase and has nonsingular high-frequency gain, then there exists a linear static output feedback that minimizes a certain quadratic cost functional. The minimization of H∞ norm of the closed-loop system with output feedback is also discussed.